How to set this strange anim. keys in outliner?
The little camera and eye icons you use to change visibility in the outliner are toggling object properties.

The eye icon links to the hide property, while the camera icon links to the hide_render property and the cursor is the hide_select property.

To insert keyframes using python you set the property and then use keyframe_insert to create a keyframe with that value.

obj = bpy.context.object

obj.hide = True
obj.keyframe_insert('hide', frame=1)
obj.hide = False
obj.keyframe_insert('hide', frame=10)

obj.hide_render = True
obj.keyframe_insert('hide_render', frame=1)
obj.hide_render = False
obj.keyframe_insert('hide_render', frame=10)